Millionaire Maker blackjack side bet
Poll
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18 members have voted
Wins are based on the dealer hand. Eight decks are used and the dealer hits a soft 17. The bust card, if there is one, counts. Dealer does not draw out if all players bust. $5 minimum bet.
Six-card straight flush: $1,000,000*
Full house: 100 to 1
Three of a kind: 15 to 1
Pair: 2 to 1
* Pays only $100,000 at the Cromwell (quite the misnomer).
This may the the hardest blackjack side bet I've ever analyzed -- but I'm up to the challenge! Meanwhile, if anybody else cares to tackle this, have at it!
It would be easy to say that it would favor a low count.
I'll get back to you with an analysis. The question for the poll is would you play this side bet blind?
Question: does, for example, a dealer hand of 7,7,6 count as a pair, or does it have to be exactly two cards?
Quote: IbeatyouracesWhen we had blackjack at our charity poker room I dealt at, I dealt out A-6 of diamonds as my hand. This was from a 6 deck shoe as well.
Yeah, and if you start with the 6-5-4, you're never going to see the 3-2-A. As to the pair, if it's within the hand, it should count, as their other MM bets work that way.
Funny they don't pay quads or 5oak, when they're paying trips. I guess a paytable is what somebody says it is.
I don't like the bet. Won't be playing it.
Quote: ThatDonGuyThe problem with the analysis is, it depends on how many players there are, and what strategy they are using. The probability of all players busting (and, if any players split, all of the split hands busting), and thus the dealer being limited to two cards, needs to be taken into account.
My analysis will just assume at least one player didn't bust and I'll footnote that assumption.
Quote:Question: does, for example, a dealer hand of 7,7,6 count as a pair, or does it have to be exactly two cards?
That counts as a pair. As long as there is a pair in there somewhere.
Is a five card straight flush actually a losing hand???
Turns out it was a little too quick - I subtracted 1 from each payout. See below for the corrected value.
Quote: tringlomaneIs that really the full paytable? What about 5 card straights and flushes? What about four of a kind? 5 of a kind? 5-card straight flush?
Yes. I saw it with my own eyes on Monday.
Quote:Is a five card straight flush actually a losing hand???
Yes.
Quote: ThatDonGuyA quick simulation of about 110 million hands, using the 1,000,000 payout for the suited A-6, shows a house edge of...
Turns out it was a little too quick - I subtracted 1 from each payout. See below for the corrected value.
The correct value, after 320 million hands, is about 15%.
Here's what I get for the calculated values:
Jackpot Probability = 2.21653016730404E-08 (1 in 45,115,560)
Full House Probability = 0.000883390523457394 (1 in 1132)
Trips Probability = 0.00891848362078757 (1 in 112)
Pair Probability = 0.197838006742154
Loss Probability = 0.792360096948299
House Edge = 15.2402475133398%
If I am calculating the variance correctly, it is about 22,179, just about all of which is caused by the jackpot
Quote: ThatDonGuyThe correct value, after 320 million hands, is about 15%.
Here's what I get for the calculated values:
Jackpot Probability = 2.21653016730404E-08 (1 in 45,115,560)
Full House Probability = 0.000883390523457394 (1 in 1132)
Trips Probability = 0.00891848362078757 (1 in 112)
Pair Probability = 0.197838006742154
Loss Probability = 0.792360096948299
House Edge = 15.2402475133398%
I agree with the probabilities to within a very small margin. Here is my return table based on a $1,000,000 at a $5 bet.
| Event | Pays | Probability | Return |
|---|---|---|---|
| Straight flush | 200000 | 0.00000002216530 | 0.00443306 |
| Full house | 100 | 0.00088339052300 | 0.088339052 |
| Three of a kind | 15 | 0.00891848362100 | 0.133777254 |
| Pair | 2 | 0.19783800674281 | 0.395676013 |
| Loser | -1 | 0.79236009694789 | -0.792360097 |
| Total | 1.00000000000000 | -0.170134716 |
Can I trouble you to double check the house edge, assuming your probabilities are correct? Perhaps you didn't adjust that a $1,000,000 net win on a $5 bet is equivalent to a pay of 200,000 to 1?
Quote: WizardCan I trouble you to double check the house edge, assuming your probabilities are correct? Perhaps you didn't adjust that a $1,000,000 net win on a $5 bet is equivalent to a pay of 200,000 to 1?
I didn't realize the $1 million was only for a $5 bet - I assumed all bets were $1. That would increase the house edge by 800,000 / 45,115,560, which makes it pretty much match your number.
Quote: ThatDonGuyI didn't realize the $1 million was only for a $5 bet - I assumed all bets were $1. That would increase the house edge by 800,000 / 45,115,560, which makes it pretty much match your number.
Thank you for your confirmation on this! I owe you another beer. I believe that makes it three?
Quote: WizardYes. I saw it with my own eyes on Monday.
I feel like someone really messed up the paytable stricture then. People will complain quick when dealers get 5 card poker hands that lose.
Quote: tringlomaneI feel like someone really messed up the paytable stricture then. People will complain quick when dealers get 5 card poker hands that lose.
I think the casinos would argue that Caesars properties already has Millionaire Maker side bets on other poker-based games and the straight flush pay was in keeping with that theme.
I've only played MM on the 6-card bet in 3CP. IIRC, it pays lesser amounts for all pat poker hands. Do the MM side bets for their other games pay for pat hands? If so, I'm with Tring on this one.Quote: WizardI think the casinos would argue that Caesars properties already has Millionaire Maker side bets on other poker-based games and the straight flush pay was in keeping with that theme.
If the dealer deals himself 2-6 or a 5-card flush, the side-betting folks are going to get upset.Quote: tringlomaneI feel like someone really messed up the paytable stricture then. People will complain quick when dealers get 5 card poker hands that lose.
Quote: JoemanIf the dealer deals himself 2-6 or a 5-card flush, the side-betting folks are going to get upset.
Don't tell me -- I didn't have anything to do with it.
Quote: JoemanI've only played MM on the 6-card bet in 3CP. IIRC, it pays lesser amounts for all pat poker hands. Do the MM side bets for their other games pay for pat hands? If so, I'm with Tring on this one.
As far as I know they all had the same paytable (except some evil properties only paid 100k on the super royal in diamonds) until now because they always made enough cards for a 6 card hand.
Now obviously I don't expect straights, flushes, four of a kinds, or straight flushes to pay the same as the other games where 6 cards are always given, but not including them at all is really shortsighted imo. Rarer poker combinations should have been included.
Quote: MBAny idea what the edge would be if the true count is very negative? Of course, we shouldn't even be at the table in that case...
I haven't looked at that. Clever, or accidental, of them to create a side bet that does better in negative counts.
Quote: WizardI haven't looked at that. Clever, or accidental, of them to create a side bet that does better in negative counts.
If you had to bet, would you pick "clever" or "accidental"?
Quote: ThatDonGuySome quick (and unverified) simulating shows that there is an AP if the TC is -7 or lower; -6 is pretty much a wash.
-7 is for eight decks. With six decks, -8 appears to be the magic number.
Quote: WizardHere is my new page on Millionaire Maker. As always, I welcome all comments, questions, and especially corrections.
1. For purposes...the player('s bet) is...
Is the original $5 bet kept if the bet is won?
